Changeset 78f02c3 in sasview for src/sas/invariant
- Timestamp:
- Feb 14, 2015 12:12:40 PM (10 years ago)
- Branches:
- master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, costrafo411, magnetic_scatt, release-4.1.1, release-4.1.2, release-4.2.2, release_4.0.1, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
- Children:
- 898a8b9
- Parents:
- 3e2ebbb
- Location:
- src/sas/invariant/media
- Files:
-
- 2 edited
Legend:
- Unmodified
- Added
- Removed
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src/sas/invariant/media/invariant_help.rst
r37bbd5f r78f02c3 1 1 ..invariant_help.rst 2 3 .. This is a port of the original SasView html help file to ReSTructured text 4 .. by S King, ISIS, during SasView CodeCamp-III in Feb 2015. 2 5 3 6 Invariant Calculation Perspective 4 7 ================================= 5 8 6 Placeholder for invariant help 9 1. Scattering Invariant_ 10 2. Volume Fraction_ 11 3. Specific Surface Area_ 12 4. Definitions_ 13 5. Reference_ 14 6. How to Use_ 15 16 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 17 18 .. _Scattering Invariant: 19 20 Scattering Invariant 21 -------------------- 22 23 The scattering invariant (Q*) is a model-independent quantity that can be 24 easily calculated from scattering data. 25 26 For two phase systems, the scattering invariant, Q*, is defined as the 27 integral of the square of the wave transfer (q) multiplied by the scattering 28 cross section over the full range of q. 29 30 Q* is given by the following equation 31 32 .. image:: image001.gif 33 34 This model independent quantity (Q*) is calculated from the scattering data 35 that can be used to determine the volume fraction and the specific area of the 36 sample under consideration. 37 38 These quantities are useful in their own right and can be used in further 39 analysis. With this scattering invariant module users will also be able to 40 determine the consistency of those properties between data. There is no real 41 data defined from zero to infinity, there usually have limited range. 42 43 Q* is not really computed from zero to infinity. Our maximum q range is 44 1e-5 ~ 10 (1/Angstrom). The lower and/or higher q range than data given can be 45 extrapolated by fitting some data nearby. 46 47 The scattering invariant is computed as follows 48 49 *I(q)* = *I(q)* w/o background : If the data includes a background, user sets 50 the value to subtract the background for the Q* computation. 51 52 Reset *I(q)* = *I(q)* scaling factor* , delta *I(q) =* delta *I(q)*scaling 53 factor* : If non-zero scaling factor is given, it will be considered. 54 55 Invariant 56 57 .. image:: image001.gif 58 59 where *g =q* for the pinhole geometry and *g =qv* (the slit height) for the 60 slit geometry which can be given in data or as a value. 61 62 Higher q-region (\>= qmax in data) 63 64 Power law (w/o background term) function = C/q4will be used 65 66 where the constant C(=2pi(delta(rho))Sv) is to be found by fitting part of 67 data with the range of qN-mto qN(m\<N). 68 69 Lower q-region (\<= qmin in data): 70 71 Guinier function = *I0exp(-Rg2q2/3)* where I0and Rgare obtained by fitting, 72 73 similarly to the high q region above. 74 75 Power law can also be used. 76 77 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 78 79 .. _Volume Fraction: 80 81 Volume Fraction 82 --------------- 83 84 .. image:: image002.gif 85 86 where delta(rho) is the SLD contrast of which value is given by users. 87 88 .. image:: image003.gif 89 90 Thus 91 92 where 0 =\< *A* =\<1/4 in order for these values to be physically valid. 93 94 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 95 96 .. _Specific Surface Area: 97 98 Specific Surface Area 99 --------------------- 100 101 .. image:: image004.gif 102 103 where *A* and *Q** are obtained from previous sections, and the Porod 104 constant *Cp* is given by users. 105 106 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 107 108 .. _Definitions 109 110 Definitions 111 ----------- 112 113 Q: the magnitude of neutron (or X-ray) momentum transfer vector. 114 115 I(Q): the scattering intensity as a function of the momentum transfer Q. 116 117 Invariant total is the sum of the invariant calculated from datas q range and 118 the invariant resulting from extrapolation at low q range and at high q range 119 if considered. 120 121 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 122 123 .. _Reference: 124 125 References 126 ---------- 127 128 Chapter 2 in O. Glatter and O. Kratky, "Small Angle X-Ray Scattering", Academic 129 Press, New York, 1982 130 131 http://physchem.kfunigraz.ac.at/sm/ <http://physchem.kfunigraz.ac.at/sm/>_ 132 133 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 134 135 .. _How to Use 136 137 How to Use 138 ---------- 139 140 1. Loading data to the panel: Open the data file from File in the menu bar. 141 Select loaded data from a plot panel by highlighting that it until its color 142 turns yellow. Then right click on that the data and selects the option Compute 143 Invariant. The application automatically computes the invariant value if the 144 data loaded is valid. 145 146 2. To subtract a background or/and to rescale the data, type the values in 147 Customized Input box. 148 149 3. If you want to calculate the volume fraction and the specific surface 150 area, type the optional inputs in the customized input box, and then press 151 Compute button. 152 153 4. The invariant can also be calculated including the outside of the data Q 154 range: To include the lower Q and/or the higher Q range, check in the enable 155 extrapolation check box in Extrapolation box. If the power low is chosen, 156 the power (exponent) can be either held or fitted by checking the 157 corresponding radio button. The Npts that is being used for the extrapolation 158 can be specified. 159 160 5. If the invariant calculated from the extrapolated region is too large, it 161 will be warn in red at the top of the panel, which means that your data is not 162 proper to calculate the invariant. 163 164 6. The details of the calculation is available by clicking the Details 165 button in the middle of the panel. 166 167 .. image:: image005.gif -
src/sas/invariant/media/pr_help.rst
r37bbd5f r78f02c3 1 1 ..pr_help.rst 2 3 .. This is a port of the original SasView html help file to ReSTructured text 4 .. by S King, ISIS, during SasView CodeCamp-III in Feb 2015. 2 5 3 6 P(r) Inversion Perspective 4 7 ========================== 5 8 6 Placeholder for P(r) help 9 The inversion approach is based on Moore, J. Appl. Cryst., (1980) 13, 168-175. 10 11 P(r) is set to be equal to an expansion of base functions of the type 12 phi_n(r) = 2*r*sin(pi*n*r/D_max). 13 14 The coefficient of each base function in the expansion is found by performing 15 a least square fit with the following fit function: 16 17 chi**2 = sum_i[ I_meas(q_i) - I_th(q_i) ]**2/error**2 + Reg_term 18 19 where I_meas(q) is the measured scattering intensity and I_th(q) is the 20 prediction from the Fourier transform of the P(r) expansion. 21 22 The Reg_term term is a regularization term set to the second derivative 23 d**2P(r)/dr**2 integrated over r. It is used to produce a smooth P(r) output. 24 25 The following are user inputs: 26 27 - Number of terms: the number of base functions in the P(r) expansion. 28 29 - Regularization constant: a multiplicative constant to set the size of 30 the regularization term. 31 32 - Maximum distance: the maximum distance between any two points in the 33 system.
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